Question

(2x-1)^0.5 + (x-1)^0.5 = 5

By square rooting them twice, i can get the x = 145, 5 is the root. But when i put 145 into the equation, it turn out not to be 145(but 5 really is the root)

So how would i know which root should i choose, i mean how to prove the 145 isn't the root? Is it by just putting 145 into the equation? And when i use synthetic division on that equation with 145, i get the solution 0 ?? Does this mean synthetic division isn't applicable for some equations?

Answer 1

ok
first square both sides

Answer 2

i get x = 145 , 5 in the end but 145 isn't the root

Answer 3

how did u get that ?

Answer 4

it must 5

Answer 5

u should get 3x-2+2sqrt((x-1)(2x-1))=25

Answer 6

yes

Answer 7

then i get 0 = x^2 - 150x + 725

Answer 8

\[2\sqrt{(x-1)(2x-1)}=27-3x\]

Answer 9

square this again

Answer 10

ok I see there are two solution

Answer 11

145 and 5

Answer 12

u have to reject 145

Answer 13

so we just show them when we put 145 in the equation the result doesn't make sense?

Answer 14

yes

Answer 15

ok